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Optimal Decision Making In Energy Markets

This article presents a generalized method for multi-dimensional optimal stopping, tailored to problems that arise in electricity markets, when addressing decisions under uncertainty with Real Options Analysis. Electricity markets are highly transparent with supply and demand volumes available as high-resolution time series and with a fair transparency on production costs. Both supply and demand show strong periodic behavior in the form of, e.g., standard load profiles or similar, making mean-reverting stochastic processes with periodic time-dependent trend functions a good choice for modeling the dynamics. However, this class of problems does not fit well to established methods for optimal stopping -- e.g., reducing dimensions or making use of properties of the reward function -- and therefore, we propose an alternative, generalized approach. We derive a general form of the Hamilton-Jacobi-Bellman equation instead and propose a numerical solution via the Bellman-Howard operator iteration. We demonstrate the functionality of this approach by setting up an example which represents the retrofit of an electrolyzer to an offshore wind farm. We solve the optimal stopping problem numerically and show that the method supports decision making well on such an irreversible investment under uncertainty.